# De-multiplexer

A De-multiplexer is a combinational circuit that has only 1 input line and 2N output lines. Simply, the multiplexer is a single-input and multi-output combinational circuit. The information is received from the single input lines and directed to the output line. On the basis of the values of the selection lines, the input will be connected to one of these outputs. De-multiplexer is opposite to the multiplexer.

Unlike encoder and decoder, there are n selection lines and 2n outputs. So, there is a total of 2n possible combinations of inputs. De-multiplexer is also treated as De-mux.

There are various types of De-multiplexer which are as follows:

## 1×2 De-multiplexer:

In the 1 to 2 De-multiplexer, there are only two outputs, i.e., Y0, and Y1, 1 selection lines, i.e., S0, and single input, i.e., A. On the basis of the selection value, the input will be connected to one of the outputs. The block diagram and the truth table of the 1×2 multiplexer are given below.

### Block Diagram: ### Truth Table: The logical expression of the term Y is as follows:

Y0=S0'.A
Y1=S0.A

Logical circuit of the above expressions is given below: ## 1×4 De-multiplexer:

In 1 to 4 De-multiplexer, there are total of four outputs, i.e., Y0, Y1, Y2, and Y3, 2 selection lines, i.e., S0 and S1 and single input, i.e., A. On the basis of the combination of inputs which are present at the selection lines S0 and S1, the input be connected to one of the outputs. The block diagram and the truth table of the 1×4 multiplexer are given below.

### Block Diagram: ### Truth Table: The logical expression of the term Y is as follows:

Y0=S1' S0' A
y1=S1' S0 A
y2=S1 S0' A
y3=S1 S0 A

Logical circuit of the above expressions is given below: ## 1×8 De-multiplexer

In 1 to 8 De-multiplexer, there are total of eight outputs, i.e., Y0, Y1, Y2, Y3, Y4, Y5, Y6, and Y7, 3 selection lines, i.e., S0, S1and S2 and single input, i.e., A. On the basis of the combination of inputs which are present at the selection lines S0, S1 and S2, the input will be connected to one of these outputs. The block diagram and the truth table of the 1×8 de-multiplexer are given below.

### Block Diagram: ### Truth Table: The logical expression of the term Y is as follows:

Y0=S0'.S1'.S2'.A
Y1=S0.S1'.S2'.A
Y2=S0'.S1.S2'.A
Y3=S0.S1.S2'.A
Y4=S0'.S1'.S2 A
Y5=S0.S1'.S2 A
Y6=S0'.S1.S2 A
Y7=S0.S1.S3.A

Logical circuit of the above expressions is given below: ### 1×8 De-multiplexer using 1×4 and 1×2 de-multiplexer

We can implement the 1×8 de-multiplexer using a lower order de-multiplexer. To implement the 1×8 de-multiplexer, we need two 1×4 de-multiplexer and one 1×2 de-multiplexer. The 1×4 multiplexer has 2 selection lines, 4 outputs, and 1 input. The 1×2 de-multiplexer has only 1 selection line.

For getting 8 data outputs, we need two 1×4 de-multiplexer. The 1×2 de-multiplexer produces two outputs. So, in order to get the final output, we have to pass the outputs of 1×2 de-multiplexer as an input of both the 1×4 de-multiplexer. The block diagram of 1×8 de-multiplexer using 1×4 and 1×2 de-multiplexer is given below. ## 1 x 16 De-multiplexer

In 1×16 de-multiplexer, there are total of 16 outputs, i.e., Y0, Y1, …, Y16, 4 selection lines, i.e., S0, S1, S2, and S3 and single input, i.e., A. On the basis of the combination of inputs which are present at the selection lines S0, S1, and S2, the input will be connected to one of these outputs. The block diagram and the truth table of the 1×16 de-multiplexer are given below.

### Block Diagram: ### Truth Table: The logical expression of the term Y is as follows:

Y0=A.S0'.S1'.S2'.S3'
Y1=A.S0'.S1'.S2'.S3
Y2=A.S0'.S1'.S2.S3'
Y3=A.S0'.S1'.S2.S3
Y4=A.S0'.S1.S2'.S3'
Y5=A.S0'.S1.S2'.S3
Y6=A.S0'.S1.S2.S3'
Y7=A.S0'.S1.S2.S3
Y8=A.S0.S1'.S2'.S3'
Y9=A.S0.S1'.S2'.S3
Y10=A.S0.S1'.S2.S3'
Y11=A.S0.S1'.S2.S3
Y12=A.S0.S1.S2'.S3'
Y13=A.S0.S1.S2'.S3
Y14=A.S0.S1.S2.S3'
Y15=A.S0.S1.S2'.S3

Logical circuit of the above expressions is given below: ### 1×16 de-multiplexer using 1×8 and 1×2 de-multiplexer

We can implement the 1×16 de-multiplexer using a lower order de-multiplexer. To implement the 1×16 de-multiplexer, we need two 1×8 de-multiplexer and one 1×2 de-multiplexer. The 1×8 multiplexer has 3 selection lines, 1 input, and 8 outputs. The 1×2 de-multiplexer has only 1 selection line.

For getting 16 data outputs, we need two 1×8 de-multiplexer. The 1×8 de-multiplexer produces eight outputs. So, in order to get the final output, we need a 1×2 de-multiplexer to produce two outputs from a single input. Then we pass these outputs into both the de-multiplexer as an input. The block diagram of 1×16 de-multiplexer using 1×8 and 1×2 de-multiplexer is given below. ### Feedback   